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  <title>Measurement of the Polarization Amplitudes of the
B&lt;sup&gt;0&lt;/sup&gt;&lt;sub&gt;s&lt;/sub&gt; --&gt; &#966; decay</title>
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<center><font color="#0000aa" size="+4">First
Measurement of the Polarization Amplitudes of the <br>
B</font>
<font color="#0000aa" size="+4"><sup>0</sup><sub>s</sub> &#8594; &#966;&#966; decay
</font></center>
<p>
Using&nbsp; CDF II data collected by the Two Track Trigger in the
period starting from March 2001 untill April 2008 corresponding to an
integrated luminosity of 2.9 fb<sup>-1</sup> we have performed
the&nbsp; first measurement of the polarization amplitudes for the
charmless in B<sup>0</sup><sub>s</sub> &#8594; &#966;&#966; &#8594; [K<sup>+</sup>K<sup>-</sup>][K<sup>+</sup>K<sup>-</sup>]
decays of the B<sup>0</sup><sub>s</sub> meson.<br>
The results are obtained with an unbinned Maximum Likelihood fit to the
reconstructed B<sup>0</sup><sub>s </sub>candidate mass and three
angular variables in a sample containing approximately 300 signal
events.
<!-- <b><br>
A more detailed description of this analysis can be found in </b>
<a href="cdf_pub_note_10120.pdf">CDF Public Note 10120</a>. </p> --></p>
<p>We have used the same data as in the updated measurement of the B<sup>0</sup><sub>s</sub>
&#8594; &#966;&#966; branching ratio (<a
 href="http://www-cdf.fnal.gov/physics/new/bottom/090618.blessed-Bsphiphi2.9/">BR
update</a>). Details on event selection are reported&nbsp; in
<a
 href="http://www-cdf.fnal.gov/physics/new/bottom/090618.blessed-Bsphiphi2.9/cdf10064_BsPhiPhi_BR.pdf">CDF
note 10064.</a>&nbsp; We measure the <b>polarization fractions</b> and
the cosine of <b>&#948;<sub>|| </sub>= arg (A<sub>//</sub>A<sub>0</sub><sup>*</sup>)
</b>for B<sup>0</sup><sub>s</sub> &#8594; &#966;&#966; as:</p>
<center>&nbsp;
<hr width="50%">
<table>
  <tbody>
    <tr>
      <td>|A<sub>0</sub>|<sup>2</sup></td>
      <td>=</td>
      <td>0.348&plusmn;0.041</td>
      <td>(stat)</td>
      <td>&plusmn;0.021</td>
      <td>(syst)</td>
    </tr>
    <tr>
      <td>|A<sub>||</sub>|<sup>2</sup></td>
      <td>=</td>
      <td>0.287&plusmn;0.043</td>
      <td>(stat)</td>
      <td>&plusmn;0.011</td>
      <td>(syst)</td>
    </tr>
    <tr>
      <td>|A<sub><font face="Symbol">^</font></sub>|<sup>2</sup></td>
      <td>=</td>
      <td>0.365&plusmn;0.044</td>
      <td>(stat)</td>
      <td>&plusmn;0.027</td>
      <td>(syst)</td>
    </tr>
    <tr>
      <td>cos&#948;<sub>||</sub></td>
      <td>=</td>
      <td>-0.91<sup>+0.15</sup><sub>-0.13</sub></td>
      <td>(stat)</td>
      <td>&plusmn;0.09</td>
      <td>(syst)</td>
    </tr>
  </tbody>
</table>
<hr width="50%">
and the resulting polarization fractions are:
<hr width="50%">
<table>
  <tbody>
    <tr>
      <td>f<sub>L</sub></td>
      <td>=</td>
      <td>0.348&plusmn;0.041</td>
      <td>(stat)</td>
      <td>&plusmn;0.021</td>
      <td>(syst)</td>
    </tr>
    <tr>
      <td>f<sub>T</sub></td>
      <td>=</td>
      <td>0.652&plusmn;0.041</td>
      <td>(stat)</td>
      <td>&plusmn;0.021</td>
      <td>(syst)</td>
    </tr>
  </tbody>
</table>
<hr width="50%">
</center>
<br>
We report also a similar measurement&nbsp; performed on B<sup>0</sup><sub>s</sub>&#8594;
J/&#968;&#966;&#8594; [&#956;<sup>+</sup>&#956;<sup>-</sup>][K<sup>+</sup>K<sup>-</sup>] decays
collected with the same trigger selections as the B<sup>0</sup><sub>s</sub>&#8594;
&#966;&#966; sample.<br>
&nbsp;&nbsp;
<center>
<hr width="50%">
<table>
  <tbody>
    <tr>
      <td>|A<sub>0</sub>|<sup>2</sup></td>
      <td>=</td>
      <td>0.534</td>
      <td>&plusmn;0.019(stat. only)</td>
    </tr>
    <tr>
      <td>|A<sub>||;</sub>|<sup>2</sup></td>
      <td>=</td>
      <td>0.220</td>
      <td>&plusmn;0.025(stat. only)</td>
    </tr>
  </tbody>
</table>
<hr width="50%">
</center>
which are consistent with the published one.(<a
 href="http://arxiv.org/abs/0712.2348">arXiv:0712.2348v2 [hep-ex]</a>,<a
 href="http://prl.aps.org/abstract/PRL/v100/i12/e121803">Phys.Rev.Lett.100:121803,2008</a>)
<br>
<br>
The results have been approved by CDF as of March 4th, 2010.<br>
<p>Jump to <a href="#Motivation">Motivation</a>, <a
 href="#Analysis%20Description">
Analysis Description</a>, <a href="#Results">Fit Results</a>,
<a href="#Systematics">Systematics</a>, <a href="#JpsiPhi">B<sup>0</sup><sub>s</sub>&#8594;
J/&#968;&#966; Results</a>, <a href="#TheoryComparison">Comparison with Theory</a>,
<a href="#PlotsAndTables">List of Approved Plots and Tables</a>.</p>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="Motivation"></a>Motivation</h2>
The B<sup>0</sup><sub>s</sub> &#8594; &#966;&#966; is a<b> P &#8594; VV (pseudo-scalar to
Vector Vector) </b> decay whose differential decay rate is determined
by&nbsp; three independent amplitudes corresponding to different
polarizations: longitudinal (A<sub>0</sub>) and two transverse
polarization with spins parallel (A<sub>||</sub>) and perpendicular (A<font
 face="Symbol"><sub>^</sub>)
</font>to each other. <br>
With these amplitudes we can define two amplitude fractions:<br>
<table border="0">
  <tbody>
    <tr>
      <td rowspan="3" align="left" valign="middle">the transverse
amplitude fraction</td>
      <td rowspan="3" align="center" valign="middle"><b>f<sub>T</sub></b>
      </td>
      <td rowspan="3" align="center" valign="middle">=</td>
      <td align="center" valign="middle">|A<sub>||</sub>|<sup>2</sup>+|A<font
 face="Symbol"><sub>^</sub></font>|<sup>2</sup></td>
    </tr>
    <tr>
      <td align="center" valign="middle">
      <hr></td>
    </tr>
    <tr>
      <td align="center" valign="middle">|A<sub>0</sub>|<sup>2</sup>+|A<sub>||</sub>|<sup>2</sup>+|A<font
 face="Symbol"><sub>^</sub></font>|<sup>2</sup></td>
    </tr>
    <tr>
      <td colspan="4" align="left" valign="middle">and</td>
    </tr>
    <tr>
      <td rowspan="3" align="right" valign="middle">the longitudinal
amplitude fraction</td>
      <td rowspan="3" align="center" valign="middle"><b>f<sub>L</sub></b></td>
      <td rowspan="3" align="center" valign="middle">=</td>
      <td align="center" valign="middle">|A<sub>0</sub>|<sup>2</sup></td>
    </tr>
    <tr>
      <td align="center" valign="middle">
      <hr></td>
    </tr>
    <tr>
      <td align="center" valign="middle">|A<sub>0</sub>|<sup>2</sup>+|A<sub>||</sub>|<sup>2</sup>+|A<font
 face="Symbol"><sub>^</sub></font>|<sup>2</sup></td>
    </tr>
  </tbody>
</table>
&nbsp;
<p>Due to V-A nature of weak interaction and helicity conservation in
QCD<b> f<sub>L</sub> &gt;&gt; f<sub>T</sub></b> is naively expected in
B decays to two light vector mesons.<br>
This expectation was <b>experimentally confirmed</b> by BaBar and
Belle in tree-dominated transitions like<br>
B<sup>0</sup> &#8594; &#961;<sup>+</sup> &#961;<sup>-</sup> and B<sup>+</sup> &#8594; &#961;<sup>0</sup>
&#961;<sup>+</sup>&nbsp; and
B<sup>0</sup> &#8594; &#961;<sup>0</sup> &#961;<sup>0</sup>.<br>
<br>
In contrast<b> </b>it was<b> </b>found
<b>f<sub>L</sub> &#8776; f<sub>T</sub></b> in
B<sup>+</sup> &#8594; &#966;K<sup>*+</sup> and in B<sup>0</sup> &#8594; &#966;K<sup>*0</sup>
for the b &#8594; s penguin decays.<br>
<br>
This is known as the <b>Polarization Puzzle.</b> Explanations invoking
either New Physics or sub-leading corrections to the naive expectation
within the Standard Model has been proposed. Updated predictions for
the B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; exists and can now be confronted
with experiment.<br>
</p>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="Analysis Description"></a>Analysis
Description</h2>
<p>In this analysis we look at the untagged time-integrated
differential decay rate as a function of three angular variables of the
final state decay products. The time integrated polarization fractions
are corrected for the expected lifetime difference for the CP-even and
CP-odd B<sup>0</sup><sub>s </sub>mass eigenstates <sub>&nbsp;</sub>using
world average B<sup>0</sup><sub>s&nbsp; </sub>
lifetime and width difference. Since the CDF Two Track Trigger biases
the natural decay proper time distribution of the available sample we
study the resulting bias in the polarization measurement with Monte
Carlo simulation and assign as a systematic uncertainty the full
expected effect. We validate this approach by performing a similar
measurement using&nbsp; B<sup>0</sup><sub>s</sub>&#8594; J/&#968;&#966; decays,
collected via the same trigger, and comparing results with current
experimental information on the polarization in such a decay.</p>
<p>The time-integrated differential decay rate with respect to the
final state particle decay angles depends on the three polarization
amplitudes (and their relative phase). Neglecting the tiny CP phase in
Bs mixing (as expected in the Standard Model) the only interference
allowed is between the two CP-even amplitudes A<sub>0</sub> and A<sub>||</sub>,
hence the only measurable phase is &#948;<sub>|| </sub>= arg (A<sub>//</sub>A<sub>0</sub><sup>*</sup>)<b>.
</b>Thus the rate depends only on three observables ( two polarization
amplitudes squared |A<sub>0</sub>|<sup>2</sup>,|A<sub>||</sub>|<sup>2</sup>,
and the strong phase&nbsp; &#948;<sub>||</sub>).&nbsp;&nbsp; The strength of
A<font face="Symbol"><sub>^</sub></font>can be determined from the
normalization condition: </p>
<p align="center">|A<sub>0</sub>|<sup>2</sup>+|A<sub>||</sub>|<sup>2</sup>
+ |A<sub><font face="Symbol">^</font></sub>|<sup>2 </sup>
= 1 </p>
<table style="border-width: 0pt; border-collapse: collapse;"
 id="AutoNumber1" border="1" bordercolor="#111111" cellpadding="0"
 cellspacing="0" width="100%">
  <tbody>
    <tr>
      <td style="border-style: none; border-width: medium;" width="50%">
      <img src="helang.jpg" border="0" height="335" width="510"></td>
      <td style="border-style: none; border-width: medium;" width="50%">
      <img src="transversiry.jpg" border="0" height="301" width="533"></td>
    </tr>
    <tr>
      <td style="border-style: none; border-width: medium;" width="50%">
      <p align="center">&nbsp;</p>
      <p align="left">Fig. 1 Helicity frame definition of angular
variables for a generic decay to V1 V2 with V1 decaying to particle P1
P2 and V2 to Q1 Q2. We take the K+ as P1 and Q1.</p>
      <p>&nbsp;</p>
      </td>
      <td style="border-style: none; border-width: medium;" width="50%">&nbsp;&nbsp;&nbsp;
Fig. 2 Transversity frame definition of angular variables. </td>
    </tr>
  </tbody>
</table>
<p align="center"><br>
&nbsp;</p>
<p>The fit to the mass and decay product angular distribution is
performed in the helicity base defined as in Fig.1 (in the transversity
base in the case of the&nbsp; B<sup>0</sup><sub>s</sub>&#8594; J/&#968; &#966; decay,
Fig,. 2). The time of decay is not observed and only the time
integrated rate is measured. The time integrated polarization fractions
are corrected to t=0 using the PDG 09 averages &#964;<sub>L</sub>=1.408<sup>+0.033</sup><sub>-0.030
</sub>ps and &#964;<sub>H</sub>=1.543<sup>+0.058</sup><sub>-0.060</sub>&nbsp;
ps where &#964;<sub>L,H </sub>are the lifetime of the Light and Heavy Bs
state respectively. Assuming equal production for B<sub>s</sub> and
anti-B<sub>s</sub> the differential decay rate (including acceptance)
can then be written as:</p>
<p align="center"><img src="angpdf.jpg" border="0" height="341"
 width="477"></p>
<table style="border-collapse: collapse;" id="AutoNumber4" border="1"
 bordercolor="#111111" cellpadding="0" cellspacing="0" width="86%">
  <tbody>
    <tr>
      <td width="50%">
      <p align="center"> <img src="ang_phiphi.gif" border="0"
 height="352" width="461"></p>
      </td>
      <td width="50%"> <img src="ang_psiphi.gif" border="0"
 height="336" width="405"></td>
    </tr>
  </tbody>
</table>
<p align="center">
<br>
&nbsp;</p>
<p>The background model for the angular distribution is a constant in
the
&#966; angle and is parameterized as 1+B*cos<sup>2</sup>&#952; for the &#952;<sub>1</sub>
and &#952;<sub>2</sub>. This is checked to be adequate using sideband data
and the parameter B is determined in the fit. The acceptance A(&#969;) with
&#969;=(cos&#952;<sub>1</sub>,cos&#952;<sub>2</sub>,&#966;) is calculated from Monte Carlo
simulation and is displayed below. The reconstructed mass for signal
events is parameterized with a double Gaussian as:</p>
<p align="center"><img src="MassPdf.gif" border="0" height="96"
 width="592"></p>
<p align="left">with parameters k and h fixed from Monte Carlo
simulation. The background model for the mass is a simple exponential, e<sup>-b*m</sup>,
with b a fit parameter. Finally we also fit for the background fraction
f<sub>b</sub> in the B<sup>0</sup><sub>s </sub>candidate mass fit
range&nbsp; 5.2&lt; m &lt; 5.6 GeV/c<sup>2</sup>.<br>
</p>
<p align="center"><img src="acceptance.gif" border="0" height="546"
 width="715"><br>
&nbsp;</p>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="Results"></a>Fit
Projections and Results</h2>
<p>&nbsp;</p>
<table style="border-collapse: collapse;" id="AutoNumber2" border="1"
 bordercolor="#111111" cellpadding="0" cellspacing="0" height="1659"
 width="87%">
  <tbody>
    <tr>
      <td height="426" width="50%"><a href="MassProj.pdf"> <img
 src="MassProj.gif" border="0" height="426" width="552"></a></td>
      <td height="426" width="50%"><a href="PhiProj.pdf"> <img
 src="PhiProj.gif" border="0" height="420" width="544"></a></td>
    </tr>
    <tr>
      <td height="430" width="50%"><a href="CosT1Proj.pdf"> <img
 src="CosT1Proj.gif" border="0" height="429" width="551"></a></td>
      <td height="430" width="50%"><a href="CosT2Proj.pdf"> <img
 src="CosT2Proj.gif" border="0" height="430" width="558"></a></td>
    </tr>
    <tr>
      <td height="461" width="50%">&nbsp;&nbsp; Fit results with
statistical uncertainties (click to download table)</td>
      <td height="461" width="50%"><a href="fit_estimates.pdf"> <img
 src="FitResults.jpg" border="0" height="433" width="503"></a></td>
    </tr>
    <tr>
      <td height="339" width="50%">Correlation matrix (click to
download table)</td>
      <td height="339" width="50%"><a href="correlations_matrix.pdf"> <img
 src="CorrelationMatrix.gif" border="0" height="172" width="544"></a></td>
    </tr>
  </tbody>
</table>
<p>&nbsp;</p>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="Systematics"></a>Systematic
Uncertainties</h2>
<p>Several systematic uncertainties have been studied with Monte Carlo
samples of size equal to the data sample and generated with a model
including the effect under study. The quoted uncertainty is the shift
in the mean value of the fit parameters in 1000 such
pseudo-experiments. The largest effect come from the inclusion of a
scalar non-resonant component under the phi meson mass peak. This has
been studied generating a B<sup>0</sup><sub>s</sub> &#8594; &#966; f0 and a
non-resonant B<sup>0</sup><sub>s</sub> &#8594; &#966; KK sample with branching
ratio similar to the equivalent B<sup>0</sup> decays.&nbsp; Other
important effect are related to the proper time acceptance of the
displaced track trigger that introduces a bias in the observed
polarization fraction which is dependent on the true value of the B<sup>0</sup><sub>s
</sub>width difference
&#916;&#915;. Finally, the effect related to a possible non vanishing
CP-violating phase in mixing at a level consistent with the current
world average is included.</p>
<p align="center"><a href="systematics.pdf">
<img src="Systematics.jpg" border="0" height="406" width="703"></a></p>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="JpsiPhi"></a>Cross Check:
Fit Projections and Results for B<sup>0</sup><sub>s</sub>&#8594; J/&#968; &#966; Decay</h2>
<p style="color: rgb(0, 0, 170);">&nbsp;</p>
<table style="border-collapse: collapse;" id="AutoNumber3" border="1"
 bordercolor="#111111" cellpadding="0" cellspacing="0" height="1242"
 width="87%">
  <tbody>
    <tr>
      <td height="426" width="50%"><a href="MassProj_J.pdf"> <img
 src="MassProj_J.gif" border="0" height="437" width="562"></a></td>
      <td height="426" width="50%"><a href="PhiProj_J.pdf"> <img
 src="PhiProj_J.gif" border="0" height="441" width="570"></a></td>
    </tr>
    <tr>
      <td height="430" width="50%"><a href="CosTProj_J.pdf"> <img
 src="CosTProj_J.gif" border="0" height="425" width="554"></a></td>
      <td height="430" width="50%"><a href="CosPProj_J.pdf"> <img
 src="CosPProj_J.gif" border="0" height="445" width="576"></a></td>
    </tr>
    <tr>
      <td height="44" width="50%">&nbsp;&nbsp; Fit results with
statistical uncertainties (click to download table)</td>
      <td height="44" width="50%"> <img src="JpsiPhiResults.gif"
 border="0" height="202" width="511"></td>
    </tr>
  </tbody>
</table>
<p>&nbsp;</p>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="TheoryComparison"></a>Comparison
of present measurement with SM theoretical prediction</h2>
<center>
<table border="1">
  <tbody>
    <tr>
      <td>&nbsp;</td>
      <td>f<sub>L</sub>[%]</td>
      <td>&nbsp;</td>
      <td>f<sub>T</sub>[%]</td>
      <td>&nbsp;</td>
      <td>&nbsp;</td>
    </tr>
    <tr>
      <td>CDFII experimental result 2.9pb<sup>-1</sup>&nbsp;&nbsp;&nbsp;</td>
      <td>34.8</td>
      <td>&plusmn;4.1(stat.)&plusmn;2.1(syst.)&nbsp;&nbsp;&nbsp;</td>
      <td>65.2</td>
      <td>&plusmn;4.1(stat.)&plusmn;2.1(syst.)</td>
      <td>&nbsp;</td>
    </tr>
    <tr>
      <td>QCD factorization (2008) &nbsp;&nbsp;&nbsp;</td>
      <td>34</td>
      <td>&plusmn;28</td>
      <td>66</td>
      <td>&plusmn;28</td>
      <td>A. Datta, D. London, J. Matias, M. Nagashima, A. Szynkman.<br>
      <b>Final-state Polarization in Bs Decays.</b><br>
      <a href="http://arxiv.org/abs/0802.0897">arXiv:hep-ph/0802.0897v2</a></td>
    </tr>
    <tr>
      <td>QCD factorization 1.a(2007) &nbsp;&nbsp;&nbsp;</td>
      <td>43</td>
      <td>&plusmn;0<sup>+61</sup><sub>-34</sub></td>
      <td>57</td>
      <td>&plusmn;0<sup>+61</sup><sub>-34</sub></td>
      <td>M.Beneke,J. Rohrerand D.Yang,<br>
      <b>Branching fractions, polarization and asymmetries of B&#8594;VV
decays.</b><br>
      <a href="http://www.sciencedirect.com/science/journal/05503213"><i>Nuclear
physics B</i>,vol. 774(Issues 1-3):pgs.64-101,9 July 2007</a>
or <a href="http://arxiv.org/pdf/hep-ph/0612290v2">arXiv:hep-ph/0612290v2</a></td>
    </tr>
    <tr>
      <td>QCD factorization 1.b(2007)&nbsp;&nbsp;&nbsp;</td>
      <td>48</td>
      <td>&plusmn;0<sup>+26</sup><sub>-27</sub></td>
      <td>52</td>
      <td>&plusmn;0<sup>+26</sup><sub>-27</sub></td>
      <td>idem</td>
    </tr>
    <tr>
      <td>QCD factorization 2&nbsp;&nbsp;&nbsp;</td>
      <td>86.6</td>
      <td>&nbsp;</td>
      <td>13.4</td>
      <td>&nbsp;</td>
      <td>Xinquiang Li,Gongru Lu, Yadong Yang,<br>
      <b>Charmless B&#8594;VV decays in QCD Factorization.</b><br>
      <i><a href="http://prd.aps.org/abstract/PRD/v71/i1/e019902">Phys.
Rev. D</a></i><a href="http://prd.aps.org/abstract/PRD/v71/i1/e019902">
71, 019902(E) (2005)</a></td>
    </tr>
    <tr>
      <td>NAIVE factorization&nbsp;&nbsp;&nbsp;</td>
      <td>88.3</td>
      <td>&nbsp;</td>
      <td>11.7</td>
      <td>&nbsp;</td>
      <td>idem</td>
    </tr>
    <tr>
      <td>NLO EWP 1&nbsp;&nbsp;&nbsp;</td>
      <td>86.3</td>
      <td>&nbsp;</td>
      <td>13.7</td>
      <td>&nbsp;</td>
      <td>D.Du and L.Guo,<br>
      <b>Electroweak penguin contributions in charmless B&#8594;VV decays
beyond leading logarithms</b><br>
      <i><a href="http://iopscience.iop.org/0954-3899/23/5/006">J.Phys.G
23, 525.(1997)</a></i>,</td>
    </tr>
    <tr>
      <td>NLO EWP 2&nbsp;&nbsp;&nbsp;</td>
      <td>86.3</td>
      <td>&nbsp;</td>
      <td>13.7</td>
      <td>&nbsp;</td>
      <td>idem</td>
    </tr>
    <tr>
      <td>Perturbative QCD&nbsp;&nbsp;&nbsp;</td>
      <td>61.9</td>
      <td><sup>+3.6+2.5+0</sup><sub>-3.2-3.3-0</sub></td>
      <td>38.1</td>
      <td><sup>+3.6+2.5+0</sup><sub>-3.2-3.3-0</sub></td>
      <td>Ahmed Ali,Gustav Kramer,Ying Li, Cai-Dian lu, Yue Long Shen,
Wei Wang and Yu-Ming Wang <br>
      <b>Charmless nonleptonic B<sub>s</sub> decays to PP, PV and VV
final state in the pQCD approach.</b><br>
      <a href="http://prd.aps.org/abstract/PRD/v76/i7/e074018"><i>Phys.
Rev. D 76, 074018 (2007)</i></a></td>
    </tr>
  </tbody>
</table>
</center>
<hr color="#800000" size="4">
<h2 style="color: rgb(0, 0, 170);"><a name="PlotsAndTables"></a>List of
Public Plots and Tables&nbsp; </h2>
<ul>
  <li>B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; fit projection 1:&nbsp; invariant
mass (<a href="MassProj.gif">gif</a>),(<a href="MassProj.pdf">pdf</a>)</li>
  <li>B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; fit projection 2:&nbsp; &#966; angle (<a
 href="PhiProj.gif">gif</a>),(<a href="PhiProj.pdf">pdf</a>)</li>
  <li>B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; fit projection 3:&nbsp; cos&#952;<sub>1</sub>
(<a href="CosT1Proj.gif">gif</a>),(<a href="CosT1Proj.pdf">pdf</a>)</li>
  <li>B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; fit projection 4:&nbsp; cos&#952;<sub>1</sub>
(<a href="CosT2Proj.gif">gif</a>),(<a href="CosT2Proj.pdf">pdf</a>)</li>
  <li>pull distributions 1&nbsp; (<a href="pulls_plot_1.gif">gif</a>) (<a
 href="pulls_plot_1.pdf">pdf</a>) </li>
  <li>pull distributions 2&nbsp; (<a href="pulls_plot_2.gif">gif</a>) (<a
 href="pulls_plot_2.pdf">pdf</a>)</li>
  <li>pull table&nbsp; (<a href="pulls_table.gif">gif</a>) (<a
 href="pulls_table.pdf">pdf</a>)</li>
  <li>Fit Results (<a href="fit_estimates.gif">gif</a>) (<a
 href="fit_estimates.pdf">pdf</a>)</li>
  <li>Correlation Matrix (<a href="correlations_matrix.gif">gif</a>) (<a
 href="correlations_matrix.pdf">pdf</a>)</li>
  <li>
    <p>Angular sculpting for B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; events cos&#952;<sub>1</sub>(<a
 href="sculptCT1.gif">gif</a>) (<a href="sculptCT1.pdf">pdf</a>), cos&#952;<sub>2
    </sub>(<a href="sculptCT2.gif">gif</a>) (<a href="sculptCT2.pdf">pdf</a>),
&#966; (<a href="sculptPhi.gif">gif</a>) (<a href="sculptPhi.pdf">pdf</a>)</p>
    <p>&nbsp; </p>
  </li>
  <li>|A<sub>0</sub>|<sup>2</sup>&nbsp; vs |A<sub>||</sub>|<sup>2 </sup>
confidence region&nbsp; (<a href="a0a1.gif">gif</a>) (<a href="a0a1.pdf">pdf</a>)&nbsp;
  </li>
  <li>|A<sub>0</sub>|<sup>2</sup>&nbsp; vs cos(&#948;<sub>||</sub>)
confidence region&nbsp; (<a href="A0cos.gif">gif</a>) (<a
 href="A0cos.pdf">pdf</a>)</li>
  <li>|A<sub>||</sub>|<sup>2</sup>&nbsp; vs cos(&#948;<sub>||</sub>)<sup>&nbsp;
    </sup> confidence region&nbsp; (<a href="A1cos.gif">gif</a>) (<a
 href="A1cos.pdf">pdf</a>)</li>
</ul>
<p>&nbsp;</p>
<ul>
  <li>P<sub>T</sub> for K<sup>+</sup> in B<sup>0</sup><sub>s</sub> &#8594; &#966;
&#966; candidate events (<a href="pt_Kplus.gif">gif</a>) (<a
 href="pt_Kplus.pdf">pdf</a>)</li>
  <li>P<sub>T</sub> for K<sup>-</sup>&nbsp; in B<sup>0</sup><sub>s</sub>
&#8594; &#966; &#966; candidate events (<a href="pt_Kminus.gif">gif</a>) (<a
 href="pt_Kminus.pdf">pdf</a>)</li>
</ul>
<p>&nbsp;</p>
<ul>
  <li>B<sup>0</sup><sub>s</sub>&#8594; J/&#968;&#966; fit projection 1 :invariant mass (<a
 href="MassProj_J.gif">gif</a>),(<a href="MassProj_J.pdf">pdf</a>)</li>
  <li>B<sup>0</sup><sub>s</sub>&#8594; J/&#968;&#966; fit projection 2: &#966; angle (<a
 href="PhiProj_J.gif">gif</a>),(<a href="PhiProj_J.pdf">pdf</a>)</li>
  <li>B<sup>0</sup><sub>s</sub>&#8594; J/&#968;&#966; fit projection 3: cos&#952;(<a
 href="CosTProj_J.gif">gif</a>),(<a href="CosTProj_J.pdf">pdf</a>)</li>
  <li>B<sup>0</sup><sub>s</sub>&#8594; J/&#968;&#966; fit projection 4: cos&#968; (<a
 href="CosPProj_J.gif">gif</a>),(<a href="CosPProj_J.pdf">pdf</a>)</li>
  <li>
    <p>Angular sculpting for B<sup>0</sup><sub>s</sub> &#8594; &#966; &#966; events
cos&#952; (<a href="cosTheta_sculpt_jp.gif">gif</a>) (<a
 href="cosTheta_sculpt_jp.pdf">pdf</a>), cos&#968; <sub> </sub>
(<a href="cosPsi_sculpt_jp.gif">gif</a>) (<a href="cosPsi_sculpt_jp.pdf">pdf</a>),
&#966; (<a href="phi_sculpt_jp.gif">gif</a>) (<a href="phi_sculpt_jp.pdf">pdf</a>)</p>
  </li>
</ul>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
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